Complete phase diagram of charge-neutral graphene in the Quantum Hall regime

Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Based on a stringent assumption on symmetry-allowed interactions, previous theoretical work predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunnelling studies universally find Kekule bond order, and sometimes also charge density wave order. Recently, it was found that if one relaxes the stringent assumption mentioned above, a phase with coexisting canted antiferromagnetic and Kekule order exists in the region of the phase diagram believed to correspond to real samples. In this work we present the complete phase diagram of ν=0 graphene in the Hartree-Fock approximation, using generic symmetry-allowed interactions, assuming translation invariant ground states up to an intervalley coherence. Allowing for a sublattice potential (valley Zeeman coupling) in accordance with spin Zeeman coupling, we find numerous phases with different types of coexisting order. We conclude with a discussion of the physical signatures of the various states.